Longitudinally extending capillary grooves on the interior surface of a heat pipe conventionally have a uniform cross-sectional dimension along the length of the heat pipe. Flow resistance in a capillary groove decreases with increasing cross-sectional area of the groove. However, capillary pressure head from one end of the capillary groove to the other end thereof also decreases with increasing cross-sectional area of the groove. In general, it is desirable for flow resistance to be as low as possible, and for capillary pressure head to be as high as possible in a capillary groove. It has been conventional practice in heat pipe technology to provide a substantially constant cross-sectional dimension (i.e., a substantially constant cross-sectional area) for longitudinally extending capillary grooves on the interior surface of a heat pipe for the entire length of the heat pipe, where the value selected for the constant cross-sectional dimension of the capillary grooves is a trade-off that provides an acceptable flow resistance as well as an acceptable capillary pressure head for the particular application.